Some upper bounds on the dimension of the Schur multiplier of a pair of nilpotent Lie algebras

Authors: BEHROUZ EDALATZADEH

Abstract: Let $(L,N)$ be a pair of Lie algebras where $N$ is an ideal of the finite dimensional nilpotent Lie algebra $L$. Some upper bounds on the dimension of the Schur multiplier of $(L,N)$ are obtained without considering the existence of a complement for $N$. These results are applied to derive a new bound on the dimension of the Schur multiplier of a nilpotent Lie algebra.

Keywords: Pair of Lie algebras, Schur multiplier, nilpotent Lie algebra

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